23.2 problem Ex 3

Internal problem ID [10238]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 45. Roots of auxiliary equation complex. Page 95
Problem number: Ex 3.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]

Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 67

DSolve[y'''[x]-y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} e^{x/2} \left (\left (c_1-\sqrt {3} c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+\left (\sqrt {3} c_1+c_2\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )\right )+c_3 \\ \end{align*}